On the powers of matrices in bottleneck/fuzzy algebra

Abstract

AbstractPowers of square matrices under the operations ⊛ = max and ⊗ = min are studied. We show that the powers of a given matrix stabilize if and only if its orbits stabilize for each starting vector and prove a necessary and sufficient condition for this property using the associated graphs of the matrix. Applications of the obtained results to several special classes of matrices (including circulants) are given